1 Background

Metal surface protection from corrosion is a major concern in metallurgical industries, oil factories, environment and chemical plants. Corrosion of metals is a chemical and electrochemical reaction that occurs when metal surfaces are exposed to acidic environment such as in acidic pickling, oil well acidizing and industrial cleaning [1]. Destruction of metals and materials leads to degradation of mechanical properties which, consequently, leads to direct loss of materials strength, reduction in thickness and failure of the material [2, 3]. This failure of operating equipment and material properties due to corrosion results into an increase in production and maintenance cost and breaking down of operating equipment. The consequences of corrosion are tremendous ranging from health effect, economic effect and safety to environmental outlooks [4, 5].

Although corrosion is a natural process and cannot be completely eliminated, it can be extensively reduced by adopting some methods. The method of corrosion control adopted by many industries includes material selection, rational design, cathodic protection and the use of chemical inhibitors [6,7,8]. Among the methods adopted for controlling corrosion, the use of chemical inhibitors has been one of the most practical and economical methods in combating corrosion [9]. Inhibitors mitigate corrosion by adsorbing onto the metal surface and impeding the anodic and/or cathodic electrochemical reactions occurring at the metal-medium interface [10, 11]. Corrosion inhibitors can be divided into organic and inorganic corrosion inhibitor [12]. Organic inhibitors are preferably used over inorganic inhibitors due to their cheap availability and also, they are less toxic compare to inorganic inhibitors [13]. Organic inhibitors with heterocyclic organic structures containing pi conjugated structure and heteroatoms, like N, S, O and P, capable of adsorbing on the metal surfaces via physisorption or chemisorption adsorption, are often being most effective [14]. Commonly adopted corrosion inhibitors are organic compounds including imidazolines, azoles, Schiff bases, amines and their derived salts [15,16,17].

Arylidene-indane-1,3-diones are crucial category of organic compounds with several potential applications in materials science to medical field [18,19,20,21,22]. Arylidene-indane-1,3-dione derivatives possess antibacterial, anti-coagulant and anti-diabetes properties [23]. Their applications have also been reported in electroluminescent devices, optoelectronics, eye lens clarification agents and nonlinear optical devices [18, 24, 25].

Pluskota et al. [21] synthesized some 2-arylidene-indan-1,3-dione derivatives and checked their drug-like properties [26]. However, the electron-rich structure of these organic systems owing to the presence of π-conjugation and heteroatoms has attracted our group to investigate the corrosion inhibitive potential of these compounds in progress of our research efforts to discover organic molecule with high corrosion inhibition potential.

Computational approaches such as DFT and MD simulations are considered to be effective, versatile and trending methods of designing and rationalizing corrosion inhibition properties of small to large systems [27,28,29]. The computational method provides insight into the reactivity parameters of a molecule and the relationship between these parameters and corrosion inhibition efficiency [30]. Also, MD simulations provide insight into the orientation, adsorption and binding energy of the inhibitor molecules on metallic surface [31]. Understanding the relationship between corrosion inhibition potentials, molecular structure and adsorption mechanism of organic compounds helps in improving on exist inhibitors and/or designing new functional ones. Therefore, this work was aimed at investigating the corrosion inhibition potential of 2-(4-(substituted)arylidene)-1H-indene-1,3-dione derivatives via density functional theory and molecular dynamic (MD) simulation. The adsorption, orientation and interactions of nine indene-1,3-diones corrosion inhibitors on Fe (110) surface in hydrochloric acid solution were studied using MD simulation.

2 Methods

2.1 Density functional theory (DFT) studies

DFT is a computational tool used to predict the electronic structure of a compound. The optimization of 2-arylidene-indan-1,3-dione derivatives (Fig. 1) was done by employing DFT technique with B3LYP functional and 6-31G(d) basis set after initially running the conformal distribution to obtain the most stable conformal (lowest energy conformal) using molecular mechanics force field (MMFF) [32]. This level of theory has been described to be consistent with experimental findings [29]. The frontier molecular orbital (FMO) energies such as highest occupied molecular orbital (EHOMO), lowest unoccupied molecular orbital (ELUMO), energy gap, ∆Egap (Eq. 1), electron affinity, A (Eq. 2), ionization potential, I (Eq. 3), electronegativity, χ (Eq. 4), chemical potential, CP (Eq. 4), chemical hardness, η (Eq. 5), softness, σ (Eq. 6), global electrophilicity index, ω (Eq. 7) and the back-donation (Eq. 8) were calculated [33,34,35]. All quantum chemical calculations were carried out using the Spartan 14 software program.

$$\Delta {\text{E}}_{{{\text{gap}}}} = {\text{ E}}_{{{\text{LUMO}}}} - {\text{ E}}_{{{\text{HOMO}}}}$$
(1)
$$A \, = \, - {\text{E}}_{{{\text{LUMO}}}}$$
(2)
$$I \, = \, - {\text{E}}_{{{\text{HOMO}}}}$$
(3)
$$\chi \, = \, - C_{{\text{p}}} = \frac{I + A}{2}$$
(4)
$$\eta \, = \frac{I - A}{2}$$
(5)
$$\sigma \, = \frac{1}{\eta }$$
(6)
$$\omega = \frac{{\chi^{2} }}{2\eta }$$
(7)
$$\Delta {\text{E}}_{{{\text{back}} - {\text{donation}}}} = - \frac{\eta }{4}$$
(8)
Fig. 1
figure 1

Structures of the 2-arylidene-indan-1,3-dione derivatives (Compounds 1 to 9)

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Furthermore, the charge transfer between the corrosion inhibitor and the metal is driven by the difference in their electronegativities (and chemical potentials) when they are in contact until a balance in chemical potential is attained [36]. The number of electrons transferred (ΔN) is calculated using Eq. 9.

$$\Delta {\text{N}} = \frac{{\chi_{{{\text{Fe}}}} - \chi_{{{\text{inh}}}} }}{{2\left( {\eta_{{{\text{Fe}}}} + \eta_{{{\text{inh}}}} } \right)}}$$
(9)

The Fukui analysis plays an important role in predicting the site of nucleophilic and electrophilic attack [37]. The partial atomic charge is defined by qk(N+1) when a molecule accepts electron and by qk(N-1) when it loses an electron. For a neutral molecule, the charge on each atom is defined by qk(N). The nucleophilic, electrophilic and dual Fukui parameters were calculated using Yao’s dual descriptors as shown in Eqs. 10, 11 and 12, respectively.

$${\text{f}}_{{\text{k}}}^{ + } = \left[ {{\text{q}}_{{\text{k}}} \left( {{\text{N }} + { 1}} \right) \, - {\text{ q}}_{{\text{k}}} \left( {\text{N}} \right)} \right]\quad {\text{nucleophilic attack}}$$
(10)
$${\text{f}}_{{\text{k}}}^{ - } = \left[ {{\text{q}}_{{\text{k}}} \left( {\text{N}} \right) \, - {\text{ q}}_{{\text{k}}} \left( {{\text{N }} - { 1}} \right)} \right]\quad {\text{electrophilic attack}}$$
(11)
$$\Delta {\text{f}}_{{\text{k}}} \left( {\text{r}} \right) = {\text{f}}_{{\text{k}}}^{ + } - {\text{ f}}_{{\text{k}}}^{ - }$$
(12)

2.2 Molecular dynamics simulation

Molecular dynamics (MD) simulations were performed on all compounds under consideration to probe their interactions with iron surface using the Forcite module in the BIOVIA Materials Studio 2017. The simulation was carried out in a box of dimension (24.82 Å × 24.82 Å × 38.11 Å) with periodic boundary conditions consisting of six layers of cleaved iron Fe (110) expanded into a 10 × 10 supercell. The Fe (110) plane is considered the most stable iron surface because it is densely packed [38]. A 30 Å vacuum layer was directly placed above the iron surface and filled with each inhibitor compound and 290 H2O, 10 H3O+ and 10 Cl- molecules to replicate a real corrosive medium. The Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force field was employed to perform geometry optimization on all component structures in the box. Molecular dynamic simulations were performed in a Nose-Hoover thermostat using NVT canonical ensemble at 298 K at a time step of 1 fs and a simulation time of 300 ps. The energy of interaction, Einteraction of the compounds with the metal surface was obtained using Eq. 13:

$$E_{{{\text{interaction}}}} = E_{{{\text{total}}}} - \left( {E_{{Fe + {\text{solution}}}} + E_{{{\text{inhibitor}}}} } \right)$$
(13)

where Etotal is the single point energy of all components in the simulation box, EFe+solution is the energy of iron (110) surface and the corrosive medium and Einhibitor is the single point energy of the inhibitor. The binding energy (Ebinding) is given by Eq. 14 [39]:

$$E_{{{\text{binding}}}} = - E_{{{\text{interaction}}}}$$
(14)

3 Results

3.1 Quantum chemical calculations, HOMO, LUMO and MEP surface analyses

Recently, DFT has become a powerful tool in predicting effective organic corrosion inhibitors [40, 41]. Some quantum chemical parameters of a compound have been established to relate the corrosion inhibition efficiency with the molecular properties [42]. These quantum chemical parameters were used to correlate the corrosion inhibition potentials of nine 2-arylidene-indan-1,3-diones with the structural variations. The results of quantum chemical calculations of 2-arylidene-indan-1,3-diones are summarized in Table 1.

Table 1 The calculated quantum chemical parameters with DFT/B3LYP/6-31G(d) method
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The optimized structures of the corrosion inhibitors are shown in Fig. 2a. The HOMO and LUMO surfaces are shown in Fig. 2b and c, respectively. The molecular electrostatic potential (MEP) maps of the corrosion inhibitors are shown in Fig. 3. The MEP surface represents the local regions on the organic systems that are susceptible to nucleophilic attack (blue region) and electrophilic attack (red, orange, yellow and green region) [43].

Fig. 2
figure 2

a Optimized structures, b HOMO and c LUMO surface maps of compounds 1 to 9

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Fig. 3
figure 3

Molecular electrostatic potential (MEP) map of Compounds 1 to 9

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3.2 Fukui indices

The Fukui indices and the Mulliken charge distribution describe the local reactive sites of an organic system that are susceptible to either nucleophilic or electrophilic attacks. Tables 2, 3, 4, 5, 6, 7, 8, 9 and 10 show selected Fukui indices (fk+, fk− and ∆fk) and Mulliken charges for the anionic, neutral and cationic forms of the corrosion inhibitors 1 to 9. The Mulliken charges depict asymmetric charge distribution of the atoms. Large values of the Fukui indices (fk+ and fk−) indicate molecular softness and chemically reactive sites [44]. The condensed Fukui dual descriptor (∆fk) is a more explicit and accurate parameter than fk+ and fk− for describing local reactivities [45, 46]. Atoms with positive ∆fk are susceptible to electrophilic attack while those with negative ∆fk are susceptible to nucleophilic attack [47].

Table 2 Selected Mulliken atomic charges and Fukui functions for Compound 1
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Table 3 Selected Mulliken atomic charges and Fukui functions for Compound 2
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Table 4 Selected Mulliken atomic charges and Fukui functions for Compound 3
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Table 5 Selected Mulliken atomic charges and Fukui functions for Compound 4
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Table 6 Selected Mulliken atomic charges and Fukui functions for Compound 5
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Table 7 Selected Mulliken atomic charges and Fukui functions for Compound 6
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Table 8 Selected Mulliken atomic charges and Fukui functions for Compound 7
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Table 9 Selected Mulliken atomic charges and Fukui functions for Compound 8
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Table 10 Selected Mulliken atomic charges and Fukui functions for Compound 9
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3.3 Molecular dynamics (MD) simulation

Molecular dynamics simulations were performed on each compound to explore the stable configurations of the different inhibitor molecules and the interaction modes between each of them and the Fe (110) surface [48]. The method tends to imitate the real-life corrosion process of mild steel in a corrosive environment and also explore the processes relating to the corrosion inhibition behavior of the molecules on the metal [49]. The interaction and the binding energies of the inhibitors on Fe (110) surface in hydrochloric acid solution are reported in Table 1. The top and side view of the Fe (110)-inhibitor system in HCl(aq) medium is shown in Fig. 4.

Fig. 4
figure 4

MD simulation graphics of most stable adsorption configurations of Compounds 1 to 9 in acidic (HCl) medium on Fe (110) surface

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4 Discussion

4.1 Discussion on DFT calculations

The energies of HOMO and LUMO are crucial quantum chemical parameters that describe the reactivity and kinetic stability of a material [50,51,52]. HOMO energy value of a molecule shows the tendency of the molecule to donate electron to low-lying vacant orbitals of a metal. Therefore, the adsorption process of a molecule on a metal surface is facilitated and increased with increase in HOMO energy (EHOMO). Hence, higher HOMO energy of a molecule enhances the corrosion inhibition potential of the molecule. On the other hand, LUMO energy (ELUMO) value of a molecule indicate the tendency of a molecule to accept electron from metal atom. Decrease in (ELUMO) shows the ability of a molecule to accept electron from a metal atom. Hence, lower LUMO energy increases the corrosion inhibition efficiency of a molecule.

The EHOMO and ELUMO calculated for the compounds are shown in Table 1. From the results, the best compounds according to the EHOMO are compounds 2, 7 and 9 (with EHOMO values of −5.37, −5.42 and −5.27 eV, respectively). The EHOMO follows the order: 9 > 2 > 7 > 5 > 8 > 6 > 3 > 4 >1. High EHOMO of compound 9 and compound 2 can be related to the presence of an effective electron-donating amine group. This indicates that compounds 2, 7 and 9 possess high tendency of donating electrons to the low-lying unfilled d-orbital of the metal atom. Also, compound 2 presents well stabilized ELUMO (−2.09 eV) with good potential of back-bond formation with the metal.

The ionization potential (I) and electron affinity (A) depict the electron-donating and electron-accepting ability of the inhibitors, respectively [53]. The ease of electron donation of a corrosion inhibitor is enhanced as the ionization potential decreases. From Table 1, the corrosion inhibitors display good ionization potential which decreases in the order: 1 > 4 > 3 > 6 > 8 > 5 > 7 > 2 > 9 and follows a reverse trend with EHOMO. It could be observed that para-substitution of diphenylamine (compound 9) and dimethylamine (compound 2) on the parent structure (compound 1) significantly lowers the ionization potential possibly by destabilizing the highest filled molecular orbital. On the other hand, the electron-accepting tendency of an inhibitor increases as its electron affinity (A) increases. The A parameter is relatively high in compounds with bare phenyl and naphthalenyl substitution at 2-indene-1,3-dione position especially in compounds 1 and 6. Substitution of electron-donating groups (such as amine and methoxy moieties) on the phenyl and naphthalenyl rings decreased the electron affinity of the corrosion inhibitors possibly by destabilizing their LUMO level relative to the unsubstituted derivatives.

The energy gap (ΔEgap) and the global hardness (η) of the compounds follow the same trend. Compounds with low ΔEgap and η possess low global hardness and exhibit good anti-corrosion properties. Compounds 9 and 7 display the lowest energy gap (2.98 and 3.15 eV, respectively) and least global hardness (1.49 and 1.58 eV) which suggest their high reactivity and kinetic instability. Also, the chemical reactivity, as deduced from ΔEgap and η, will increase in the order: 9 < 7 < 2 < 6 < 5 < 8 < 4 < 3 < 1. Conversely, global softness follows a reversed trend. This trend supports the high chemical reactivity, global softness (σ), ease of electron donation and effective corrosion inhibition potentials of systems with electron-donating substituents. Similar observation has been reported in literature [54]. Interestingly, para-substitution on the benzylidene moiety of 1H-indene-1,3-dione lowers the energy gap, global hardness and improves the ionization potential, global softness, the number of electrons transferred and the back-donation properties of the organic inhibitors relative to the parent compound 1.

The electronegativity (χ) specifies the direction of flow of electron between the metal surface and the inhibitor till a balance in chemical potential is attained. On adsorption of inhibitor on the metal surface, especially iron (with electronegativity of 7 eV), electrons should be transferred from the species with lower electronegative to the one with higher electronegativity. From Table 1, all the inhibitors display less electronegativity (χ = 3.78–4.54 eV) than that of iron which suggests that they are capable of electron transfer to the metal surface. The χ follows the order: 2 < 9 < 7 < 8 < 5 < 3 < 4 < 6 < 1. The farther the χ of the inhibitor is from that of the metal, the slower the attainment of equalization of chemical potential, the better the reactivity and the greater the corrosion inhibition efficiency. This suggests that compounds 2, 9 and 7 will present good kinetic interaction with the iron surface. Also, the number of transferred electron (ΔN) is an effective quantum chemical descriptor of metal-inhibitor interactions. High ΔN suggests good interaction between the corrosion inhibitor and the iron surface. The ΔN follows an opposite trend with the energy gap, suggesting better corrosion inhibition potentials of the substituted organic systems than the parent structure (compound 1). Compound 9 displays largest ΔN indicating that it has a greater potential of releasing electron into low-lying vacant d-orbitals of the metal. Electrophilicity (ω) is a quantum chemical parameter that measures stabilization of energy as a result of maximum electron transfer between a donor and acceptor. The ω follows the trend: 2 < 8 < 7 < 3 < 9 < 4 < 5 < 1 < 6. Corrosion inhibitors with low electrophilicity exhibit good electron-releasing potential for effective interaction with and stabilization on a metal surface [55]. The back-donation character of the organic inhibitor signifies the synergistic tendency of the inhibitors to accept π-electron from the d-orbital of the iron into its vacant antibonding orbital. This property increases in the order: 1 < 3 < 4 < 8 < 5 < 6 < 2 < 7 < 9, indicating that compounds 9, 7 and 2 possess good back-bonding ability with metal surface.

Succinctly, p-methoxy and p-tolyloxy substituted inhibitors (compounds 3 and 4, respectively) display close chemical reactivity with the reference structure (compound 1), indicating little contribution of these moieties to corrosion inhibition potential while amine and dimethylnaphthalenyl moieties improved the chemical reactivity.

4.2 HOMO, LUMO and molecular electrostatic potential (MEP) surface analyses

The HOMO and LUMO maps of compounds 1 to 9 show the distribution of the frontier molecular orbitals over the structures (Fig. 2b and c). The HOMO and LUMO of compound 1 are delocalized entirely over the structure indicating that frontier orbitals available for electron donation and reception are not essentially localized. Para-substitutions on the benzylidene moiety result in HOMO re-distribution majorly over the aryl group and partly over the indene carbon-2 suggesting the region of the compounds available for electron donation into the low-lying vacant orbitals of iron. On the other hand, the LUMO is delocalized almost over the entire molecules except on the methyl (compounds 2,3,5,7), phenyl (compounds 4 and 9) and tert-butyl (compound 8) moieties. These regions depicting the least unfilled molecular orbitals of the inhibitors are possible sites available for back-bonding with the metal surface. The molecular electrostatic potential surface analyses reveal the phenyl ring, and the oxygen atoms of the phenoxy, hydroxyl, methoxy and indene carbonyl moieties as local nucleophilic sites on the inhibitors available for adsorption on the metal surface (Fig. 3). The regions with positive electrostatic potential are the phenyl hydrogen, methyl, tert-butyl and dimethylamine moieties.

4.3 Local reactivity and Fukui descriptors

In compound 1, aromatic carbon, C11, exhibits highest fk+ and fk− indicating that it is reactive site for both electrophilic and nucleophilic attacks (Table 2). However, the highly positive ∆fk (0.029) of the carbon atom (C11) indicates that it is a preferred site for nucleophilic attack on a metal surface. The olefinic carbon bridge (C10) between the 1,3-indane-dione and the aryl moieties displays maximum negative Fukui dual function (∆fk = −0.042) indicating that it is the preferred electrophilic site. Similarly, the electrophilic center on compounds 2, 3, 4, 6, 7 and 8 was located on olefinic carbon bridge, C10, with highly negative ∆fk as shown in Tables 3, 4, 5, 7, 8, 9, respectively. Compounds 5 and 9, however, exhibit active electrophilic centers at indenone oxygen O2 and phenyl carbon (C14), respectively as shown in Tables 6 and 10.

The most positive ∆fk for compound 2 is on amine nitrogen, N1, while the carbon of the methyl substituent on the amine displays maximum negative ∆fk (Table 3). Although the methoxy carbon (C17) of compounds 3 and 5 shows highly positive fk+ and fk−, the positive ∆fk are localized on the heteroatoms, O3 and O4, respectively. Likewise, the maximum positive ∆fk values of 0.045 and 0.052 are observed for the naphthalenyl carbon, C11, of compounds 6 and 7, respectively (Tables 7 and 8). The dual nucleophilic reactive sites are observed at the phenyl carbon, C11 and tert-butoxide oxygen, O3 (for compound 8), and at the phenyl carbon atoms, C13 and C15 (for compound 9), respectively. In essence, the nucleophilic sites on the corrosion inhibitors are located both on the heteroatoms and the sp2-hybridized carbon atoms, while the olefinic carbon bridge majorly behaves as an electrophilic center available for possible back-bonding with the metal surface. Effective metal-inhibitor interactions enhance adsorption of the inhibitor and, consequently, the isolation of the metal from the corroding medium.

4.4 Adsorption and binding energy of iron-inhibitor system

Figure 4 represents the top and side views of the interaction of the molecules with the Fe (110) in the presence of the molecules and ions of the corrosive solvent (H2O, H3O+ and Cl−). It is noted that each of the inhibitor molecules positioned itself closer to the surface of the metal and orientating itself in a flat configuration that is partially or completely parallel to the surface after equilibration for 300 ps at 298 K. Thus, the flat configuration of the molecules ensures that the metal surface is well covered and protected from the corrosive medium [56]. This is as a result of electron-donation from active centers of the molecules, such as N, O, phenyl rings, to the d-orbitals of iron [57].

The interaction energy of each of the molecules is reported in Table 11. The negative values of the interaction energies of the molecules indicate that the interaction between them and the metal substrate is exothermic in nature. On the other hand, the binding energy of adsorption to the metal surface is the negative of the interaction energy. The more negative the interaction energy, the more positive the binding energy and the more the molecule easily adsorbs on the steel surface. From Table 11, all the corrosion inhibitors exhibit good binding affinity for the iron (110) surface in the corroding medium. Remarkably strong binding energies were obtained for compounds 2, 4, 7 and 8. However, compound 7 displays the largest binding energy compared to other selected molecules, indicating that it adsorbs most easily to the mild steel surface and provides the best protection for the surface against the corrosive chloride medium. This observation may be attributed to good structural planarity, effective back-donation tendency, high electron affinity, chemical softness of the naphthalene-based inhibitor and its proximal alignment on the iron surface (Fig. 4). Also, steric hindrance due to the diphenyl rings may hamper the iron-inhibitor interaction between the Fe (110) surface and compound 9, thereby relatively weakening inhibitor’s adsorption potential [58,59,60,61].

Table 11 Interaction (adsorption) and binding energies of inhibitor molecules with Fe (110) surface in hydrochloric acid medium
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5 Conclusions

Corrosion inhibition potentials of nine derivatives of 1H-indene-1,3-dione have been studied using quantum chemical calculations and molecular dynamics approach. The compounds exhibit low energy gap, global hardness, ionization potential, electrophilicity and high electron affinity, global softness, back-donation and number of transferred electrons suggesting good corrosion mitigation potentials. Compounds 2, 7 and 9 display uniquely low energy gap suggesting their high chemical reactivity and kinetic instability. The electrostatic potential map and the condensed Fukui dual descriptor suggest asymmetrical charge distribution with nucleophilic reactive sites located essentially on the heteroatoms and the carbon atoms of phenyl and naphthalenyl moieties. The strong binding energy (89.93–237.83 kJ/mol) between the iron surface and the 2-(4-(substituted)arylidene)-1H-indene-1,3-diones and the effective surface coverage indicate good anti-corrosion potentials. Compound 7 (2-((4,7-dimethylnaphthalen-1-yl)methylene)-1H-indene-1,3(2H)-dione), however, exhibits strongest binding with Fe(110) surface implying its effective adsorption and good anti-corrosion potentials which may be attributed to its good affinity for the iron surface and back-donation tendency. Although 2-(4-(diphenylamino)benzylidene)-1H-indene-1,3(2H)-dione (compound 9) possesses low energy gap and good reactivity, its effective adsorption on the iron surface is reduced possibly by steric hindrance provided by the diphenyl rings.